Propagation of surface elastic waves in the Cosserat medium

The problem of surface elastic wave propagation in the Cosserat medium (half-space) is considered. The strained state is characterized by two independent vectors: displacement and rotation. Solutions to the equations of motion are sought in the form of wave packets specified by an arbitrary Fourier spectrum. It is shown that, if the solution is sought in the form of a three-component displacement vector and a three-component rotation vector dependent on time, depth, and longitudinal coordinate, the initial system splits into two systems, one of which describes the Rayleigh wave and the other corresponds to a transverse wave decaying with depth. For both waves, analytical solutions in terms of displacements are obtained. It should be particularly noted that, unlike the Rayleigh wave, the solution for the transverse surface wave has no analogues in the classical elasticity theory. The transverse wave solution is numerically compared with the Rayleigh wave solution.     

Exact and approximate solutions for the electron nonsinglet structure function in QED

Two exact, valid up to infinite perturbative order, numerical solutions of the Lipatov equation for the nonsinglet electron structure function in the QED are presented. One of them is of the Monte Carlo type and another is based on the numerical inversion of the Mellin transform. They agree numerically to a very high precision (better than 0.05%). Within the leading logarithmic approximation, the exact solution is compared with the perturbative second and third order exponentiated solutions. It is shown that the perturbative second order solution inspired by the Yennie-Frautschi-Suura (exclusive) exponentiation is much closer to the exact solution than the other ones. New compact analytical formula for the third order exponentiated solution is given. It is shown to be in perfect numerical agreement with the infinite order solution of the Monte Carlo and Mellin type.     

相干瑞利散射海水水下温度测量技术的理论研究

海水水下温度的快速大范围测量是海洋监测的重要内容,在民用和军事领域都有着至关重要的意义,本文提出了采用相干瑞利散射方法测量海水水下温度的新方法:用宽带高速光电探测器接收本振激光和海水后向瑞利散射光相干产生的差频信号,进行傅里叶变换分析获取海水瑞利散射展宽谱,从而反演海水温度,首先从海水的热力学特性出发,对利用瑞利散射谱测量海水水下温度的基本原理进行了理论研究和软件模拟;然后对采用相干探测测量海水瑞利散射谱的测量方法进行了理论分析和软件模拟;在此基础上对瑞利散射海水水下温度测量精度进行了分析,得出当水体瑞利散射频谱半宽度测量精度为1 MHz时,测温精度约为0.35 K。     

Variational Approach to Uniform Rigid Rotation of Ginzburg—Landau Vortices

Time periodic solutions for the hyperbolic gauged Ginzburg–Landau system, with spatial domain the unit disc, are shown to exist. Time periodic solutions representing bound states of vortices rotating about one another have been previously obtained in the near self-dual limit, using perturbative techniques. In contrast, we here take a variational approach, the solutions being obtained as critical points of an indefinite functional. We consider a special class of solutions which map out, uniformly in time, an orbit of the rotation group SO(2). It is shown that in the limit of large coupling constant the solutions have nontrivial time dependence or, as is shown to be equivalent, are not radially symmetric in any gauge.     

矩形表面波探头声场的高斯声束叠加法

利用矩形压电晶片和有机玻璃楔块折射可激励出超声表面波,广泛用于固体近表面缺陷检测和材料特性测量.由于描述表面波三维声场的理论方法还鲜有报道,因而主要采用简化的表面波二维声场模型来定量分析这类问题.高斯声束模型近些年被广泛应用于解决超声体波传播的各种复杂问题,然而,目前还没有将其扩展应用到超声表面波的声场的计算中.通过结合表面波格林方程和矩形换能器的高斯声束模型,推导出基于高斯声束叠加的表面波三维声场解析解.进一步,将该方法与点源叠加的数值解进行了分析比较,计算结果表明表面波声场的高斯声束叠加方法在具有较好计算精度的同时,还具有更快的计算效率.     

Mie-Rayleigh Doppler Wind Lidar with Two Double-edge Interferometers

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Mesh quality effects on the accuracy of CFD solutions on unstructured meshes

The order of accuracy and error magnitude of node- and cell-centered schemes are examined on representative unstructured meshes and flowfield solutions for computational fluid dynamics. Specifically, we investigate the properties of inviscid and viscous flux discretizations for isotropic and highly stretched meshes using the Method of Manufactured Solutions. Grid quality effects are studied by randomly perturbing the base meshes and cataloguing the error convergence as a function of grid size. For isotropic grids, node-centered approaches produce less error than cell-centered approaches. Moreover, a corrected node-centered scheme is shown to maintain third order accuracy for the inviscid terms on arbitrary triangular meshes. In contrast, for stretched meshes, cell-centered schemes are favored, with cell-centered prismatic approaches in particular showing the lowest levels of error. In three dimensions, simple flux integrations on non-planar control volume faces lead to first-order solution errors, while second-order accuracy is recovered by triangulation of the non-planar faces.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Large deflection of clamped circular plate and accuracy of its approximate analytical solutions

A different set of governing equations on the large deflection of plates are derived by the principle of virtual work(PVW), which also leads to a different set of boundary conditions. Boundary conditions play an important role in determining the computation accuracy of the large deflection of plates. Our boundary conditions are shown to be more appropriate by analyzing their difference with the previous ones. The accuracy of approximate analytical solutions is important to the bulge/blister tests and the application of various sensors with the plate structure. Different approximate analytical solutions are presented and their accuracies are evaluated by comparing them with the numerical results. The error sources are also analyzed. A new approximate analytical solution is proposed and shown to have a better approximation. The approximate analytical solution offers a much simpler and more direct framework to study the plate-membrane transition behavior of deflection as compared with the previous approaches of complex numerical integration.     

Solitons in collisionless cold plasma

The relativistic nonlinear self-consistent equations for a collisionless plasma with stationary ions are transformed into a form appropriate for finding exact analytic solutions. It is shown that for an axial system with planar geometry, the two-dimensional stationary equations for this system can be reduced to the sh-Gordon equation. The exact solution of this equation describing the charge-density equilibrium configuration is obtained, the solution having sharp transverse boundaries and a soliton form in longitudinal direction. The generalization to the nonstationary case is considered in an perturbative approach.     

Mie-Rayleigh Doppler Wind Lidar with Two Double-edge Interferometers

The Mie-Rayleigh direct detection Doppler lidar (DDDL) with two double-edge etalons is presented. Fabry-Perot (F-P) etalon is used as the spectral analyzer for Doppler measurement formthe aerosol and molecule backscattered signals. The aerosol and molecular backscattering signals are separated by a polarization isolator with less signal decrement, so this system has about same accuracy as individual Rayleigh Doppler lidar or Mie Doppler lidar system. The simulation on a proposed ground-based DDDL at 532 nm shows that the velocity error is less than 2 m/s below 8 km for a 100 m vertical resolution by Mie channel and 2m/s up to 20 km by Rayleigh channel, respectively.     

A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

A Chebyshev–Lagrangian method for acoustic analysis of a rectangular cavity with arbitrary impedance walls

A general Chebyshev–Lagrangian method is proposed to obtain the analytical solution for a rectangular acoustic cavity with arbitrary impedance boundary conditions. The originality of the present paper is the successful attempt of applying orthogonal polynomials, such as Chebyshev polynomials of the first kind, to the analysis of a rectangular sound field with general wall impedance. The sound pressure is uniformly expressed as triplicate Chebyshev polynomial series which is independent in each direction. The Chebyshev polynomial series solution is obtained using the Rayleigh–Ritz procedure after considering the influence of boundary impedance on the cavity as the work done by the impedance surfaces in the Lagrangian function. The accuracy and reliability of the proposed method are validated against the analytical solutions and some numerical results available in the literature. Excellent orthogonality and complete properties of the Chebyshev polynomials ensure the rapid convergence, numerical stability, high accuracy of the current solution. The simplicity and low computational cost of the present approach make it preferable to obtain the results of complex models even in the relative high frequency range by choosing enough truncated terms in the sound pressure expression. Numerous cases with various uniform or non-uniform impedance boundary conditions are analyzed numerically and some of the results can be used as benchmark. It is shown that the impedance boundary condition can effectively influence or modify the acoustic characteristics and response of a cavity.     

Structural stability of a nonparaxial singular mode beam

The exact explicit solution of the Maxwell equations for nonparaxial singular beams propagating in free space or in a homogeneous isotropic medium is considered. It is shown that, in the paraxial approximation, such solutions for mode beams of both lower and higher orders may turn into the solutions for guided modes or vortices of optical fibers. It is found that a variation of the Rayleigh length for a mode beam does not change the structure of phase and polarization singularities; it merely transforms their coordinates. In the paraxial limit, the singularities are shifted off the axis to regions with negligible light fluxes.     

Bond order-bond length relationship in all-valence-electron molecular orbital theory

The time-dependent Hartree-Fock theory of molecular dynamic polarizabilities is reviewed in the context of the Dirac density operator approach. The energy ‘denominators’ are shown to vanish for external field frequencies which are solutions of an eigenvalue-equation which is the same as that arising under the random phase approximation assumptions. A perturbative approach to its solution is presented which gives good results at its lowest-order when applied to the prediction of the lowest excited singlet state of the ethylene molecule.     

Performance of dispersed Rayleigh interferometer on the active cophasing and alignment testbed

We report the laboratory experiment on a segmented mirror testbed that shows the use of a dispersed Rayleigh interferometer to phase segmented mirrors.Segment alignment of tip-tilt is fulfilled by overlapping diffraction pattern centroids of the three individual segments on the focal plane.A spherical interferometer is introduced to evaluate the performance of piston, tip-tilt sensing, and control closed-loop, and finally a total residual root-mean-square (RMS) surface error of about 45 nm is achieved, in which a typical error of about 20 nm is contributed by piston.These results demonstrate that the dispersed Rayleigh interferometer can successfully sense the piston of segmented mirrors and be used in phasing segmented telescopes under extensive studies.     

目标表面发射率对红外热像仪测温精度的影响

介绍了红外热像仪测温原理,分析了影响红外热像仪测温精度的因素,计算了不同表面发射率下红外热像仪的测温误差曲线。理论分析表明,目标表面发射率越高,红外热像仪测温精度越高。实验改变表面发射率的设置,计算了不同表面发射率对应的总辐射亮度,得到TP8型长波红外热像仪能够精确测温时,目标表面发射率必须大于0.5的结果。最后,对表面发射率分别为0.96、0.93和0.3的3种材料进行实际测温,结果表明,材料表面发射率较高时,红外热像仪具有较好的测温精度。     

Excitation of Rayleigh and Stoneley surface acoustic waves by distributed seismic sources

Using the integral Fourier-transform technique, we obtain a solution in integral form to the problem of excitation of elastic waves in a homogeneous isotropic solid half-space and the bordering homogeneous gas by the time-dependent forces which are arbitrarily distributed in a solid over the plane parallel to the interface of the media. Different configurations of the force sources are analyzed from the viewpoint of excitation of different types of seismoacoustic waves. Expressions for the time-averaged radiated powers of the Stoneley wave at the gas–solid interface and the Rayleigh wave at the solid–vacuum interface as well as analytical expressions for the Rayleigh wave displacements, which are valid for large distances from the source, are obtained for the harmonic dependence of forces on time. Excitation of a Rayleigh wave by the point sources oriented vertically, i.e., along the normal to the surface of elastic half-space, and horizontally, i.e., parallel to this surface, is analyzed in detail. Analytical expressions for the Rayleigh-wave radiated power are obtained. The dependences of these powers on the source orientation and depth are derived. It is shown that the Rayleigh-wave radiated power decreases with distance between the point of the force application and the boundary and turns to zero for a source depth of about 17.5% of the wavelength of the transverse wave in the case of a horizontally oriented subsurface source and a medium with identical Lamé parameters λ and μ. This power increases and reaches a relative maximum when the source depth becomes equal to about 42.4% of the wavelength of the transverse wave and then exponentially falls off as the source depth increases. This maximum is about 5.5% of the surface-source radiated power.     

Accuracy analysis on Rayleigh lidar measurements of atmospheric temperature based on spectroscopy

We make a detailed analysis on the linearity and accuracy of the relationship between the full-width at half-height （FWHH） of the atmosphere molecules Rayleigh scattering spectrum and the square root of the atmospheric temperature. A simulation of the FWHH of the atmosphere molecules Rayleigh scattering spectrum is made based on the S6 Atmosphere Model and U.S. Standard Atmosphere Model. The calcu- lated temperature is compared with the initial simulation temperature. The result shows that the FWHH of the atmosphere molecules Rayleigh scattering spectrum is nearly proportional to the atmospheric temperature. The goodness-of-fit index of the fitting curve is 0.9977 and the maximum absolute error of measured atmospheric temperature is about 2 K.